The series follows a specific difference logic where the differences between consecutive terms are -3, -3, -3, -3, and so on. Subtracting 3 from 9 gives the first missing term of 6, subtracting 3 from 3 gives 0, subtracting 3 from 0 gives -3, and subtracting 3 from -3 gives -6. Therefore, the missing terms are 6, 0, -3, and -6.